Locality preserving multimodal discriminative learning for supervised feature selection

Feature selection has been an important preprocessing step in high-dimensional data analysis and pattern recognition. In this paper, we propose a locality preserving multimodal discriminative learning method called LPMDL for supervised feature selection, which arises by solving two standard eigenvalue problems and seeks to find a pair of optimal transformations for two sets of multivariate data in different classes. This topic can optimally discover the local structure information of the given data hided in the original space and aims at structuring an effective low-dimensional embedding space, under which LPMDL keeps nearby data pairs in the same class close and between-class data pairs apart, and the projections of the original data in different classes can be appropriately separated from each other. LPMDL can be performed either in the input space or the reproducing kernel Hilbert space which gives rise to the kernelized version of LPMDL. We also evaluate the feasibility and efficiency of the LPMDL approach by conducting extensive data visualization and classification tasks. Experimental results on a broad range of data sets show LPMDL tends to capture the intrinsic structure characteristics of the samples data due to the effective representation of the points and achieves similar or even better performance than the conventional PCA, NPE, LPP and LFDA methods.